H. R. Dullin, P. H. Richter, A. P. Veselov, “Action variables of the Kovalevskaya top”, Regul. Chaotic Dyn., 1998, Volume 3, Issue 3,Pages <nobr>18

This article is cited in 18 papers

On the 70th birthday of J.Moser

Action variables of the Kovalevskaya top

H. R. Dullin^a, P. H. Richter^b, A. P. Veselov^cd

^a Department of Applied Mathematics, University of Colorado, Boulder
^b Institut für Theoretisclie Physik, Universität Bremen
^c Landau Institute for Theoretical Physics. Moscow, Russia
^d Department of Mathematical Sciences, Loughborough University, UK

Abstract: An explicit formula for the action variables of the Kovalevskaya top as Abelian integrals of the third kind on the Kovalevskaya curve is found. The linear system of differential equations of Picard–Fuchs type, describing the dependence of these variables on the integrals of the Kovalevskaya system, is presented in explicit form. The results are based on the formula for the actions derived by S.P. Novikov and A.P. Veselov within the theory of algebro-geometric Poisson brackets on the universal bundle of hyperelliptic Jacobians.

MSC: 34A05, 58F07

Received: 16.06.1998

Language: English

DOI: 10.1070/RD1998v003n03ABEH000077